# 7.1.5 Gravitational Field Strength in a Radial Field

### Gravitational Field Strength in a Radial Field

• The gravitational field strength, g at a point describes how strong or weak a gravitational field is at that point
• g in a radial field (such as a planet) is calculated using the equation: • Where:
• g = gravitational field strength (N kg-1)
• G = Newton’s Gravitational Constant
• M = mass of the body producing the gravitational field (kg)
• r = distance from the mass where you are calculating the field strength (m)
• Gravitational field strength, g, is a vector quantity
• The direction of g is always towards the centre of the body creating the gravitational field
• This is the same direction as the gravitational field lines
• On the Earth’s surface, g has a constant value of 9.81 N kg-1
• However, outside the Earth’s surface, g is not constant
• g decreases as r increases by a factor of 1/r2
• This is an inverse square law relationship with distance

• When g is plotted against the distance from the centre of a planet, r has two parts:
• When r < R, the radius of the planet, g is directly proportional to r
• When r > R, g is inversely proportional to r2 (this is an ‘L’ shaped curve and shows that g decreases rapidly with increasing distance r)
• Sometimes, g is referred to as the ‘acceleration due to gravity’ with units of m s-2
• Any object that falls freely in a uniform gravitational field on Earth has an acceleration of 9.81 m s-2

#### Worked Example

The mean density of the Moon is 3/5 times the mean density of the Earth.

The gravitational field strength on the Moon is 1/6 of the value on Earth.

Determine the ratio of the Moon’s radius rM and the Earth’s radius rE.  #### Exam Tip

Remember that r is always taken from the centre of mass of the object creating the gravitational field.

Also, make sure you’re comfortable with drawing the inverse square law graph of against r, since this is a common exam question

Close Close

# ## Download all our Revision Notes as PDFs

Try a Free Sample of our revision notes as a printable PDF.

Already a member?